This invention pertains to methods and arrangements for attaining high beta values in plasma confinement devices. More specifically, this invention pertains to methods for accessing the second stability region of operation in toroidal magnetic confinement devices.
The performance of a magnetic confinement device can be expressed by the parameter beta .beta., the ratio of the plasma kinetic pressure to the confining pressure of the magnetic field. Beta is a direct measure of the efficiency of the magnetic confinement; that is, high-.beta. systems make better use of the confining field than do low-.beta. systems. Beta is defined as: ##EQU1## where p.sub.av =.intg.pd.tau./.intg.d.tau. and B.sub.av.sup.2 =.intg.B.sup.2 d.tau./.intg.d.tau., the integration being over the plasma volume, where p.sub.av is the average plasma pressure and B.sub.av.sup.2 /2 is the average magnetic pressure.
A plasma confined in a magnetic field may be unstable. Various instabilities have been predicted based on ideal single fluid magnetohydrodynamic (MHD) equilibrium and linear stability analyses in axisymmetric toroidal configurations. Potentially unstable MHD modes include: the ballooning modes, the Mercier modes (interchange modes), and external and internal kinks. Of these modes, ballooning and internal kinks are serious obstacles to creating and maintaining stable high-.beta. plasmas. Generally, the criteria for ideal MHD instability will depend on specific plasma parameters such as .beta., the pressure and safety factor profiles, and the various geometrical shaping factors. Consequently, stable operation has been limited to low betas. This region of operation is referred to as the "first region" of stable operation. Increasing beta beyond the limit of the first region results in operation in the unstable region where deleterious effects of unstable MHD modes are present.
Several studies have been carried out to find environments favorable for suppressing the ballooning instability mode (e.g., A. M. Todd et al., Nucl. Fusion 19 743 (1979)). An empirical shape-optimization by Miller and Moore (Phys. Rev. Lett. 43, 765 (1979)) has shown that a strongly modified dee shaped plasma with an indentation on the inside edge of the plasma (i.e., inwardly concave at the inner-major-radius side) can enhance achievable stable .beta. against ballooning for small aspect ratio configurations. Similarly, Mercier (in Lectures in Plasma Physics, EURATOM-CEA/CEN/EUR 5/27 e, EURATOM, Luxembourg, 1974) showed that an indented plasma enhanced plasma stability against localized interchange modes.
While the majority of design studies have been performed at low .beta., it has also been known that at very large .beta., there exists a region of operation where stability to ballooning modes could be regained because of the magnetic well effects produced by the large outward Shafranov shift (e.g., Coppi et al., Nucl. Fusion 19, 715 (1979)). This stable region was called the "second region" of stability and many unsuccessful attempts were made to discover operating scenarios which would make this region accessible from the low-.beta. regime. [By accessibility, we mean a demonstration that a method of operation of the device is possible whereby the .beta. (or pressure) of the device can be increased continuously from zero to a very large .beta. value without passing through the unstable region.] For example, detailed numerical calculations (e.g., Monticello et al., Sherwood Meeting, Austin, Tex., April, 1981) demonstrated that in plasmas with nearly circular cross sections the second stable region occurred only for large aspect ratio configurations and accessibility was not possible.
In addition, the internal kink has been shown to be a prime candidate responsible for enhanced fast-ion loss through "fishbone oscillations", thus limiting the ability to increase .beta..
It is therefore an object of the present invention to provide a method and apparatus for forming a magnetically confined plasma.
Another object of the present invention is to provide a method and apparatus for forming a magnetically confined plasma and avoiding plasma MHD instabilities which defeat plasma confinement.
Yet another object of the present invention is to provide a method and apparatus for forming a plasma with an increased beta.
Another object of the present invention is to provide a method and apparatus which makes accessible the second region of stability against ballooning modes.
Still another object of the present invention is to provide a method and apparatus for forming a high-beta plasma having stabilized ballooning and internal-kink modes thereby minimizing fast ion losses.
Additional objects, advantages, and novel features of the invention will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following or may be learned by practice of the invention.